Charging Issues - please help

I purchased a use macbook pro from a local mac resell/repair shop. The first one I bought had issues - hardward not connected well, they gave me another. That one has charging issues - when you plug in the charger to the unit it sometimes lights up and shows that it is charging, other times it does not. They replaced the charging port (not sure what it is called) and gave me another charger but it did the same thing especially when the macbook charge is under 60%. I took it back in today and they replicated it, cycles were high on the battery so they replaced that and gave me a new charger, told me to plug into a surge protector. I did that and it turned on the charging light and charging icon, but a few minutes later it turned off.
So odd ....anyone have any ideas what this could be?
I have not dropped the machine or spilled anything onto it.

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